1. The problem is to subtract the mixed numbers $2 \frac{3}{10}$ and $1 \frac{3}{4}$. 2. First, convert the mixed numbers to improper fractions: $$2 \frac{3}{10} = \frac{2 \times 10 + 3}{10} = \frac{20 + 3}{10} = \frac{23}{10}$$ $$1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}$$ 3. To subtract the fractions $\frac{23}{10} - \frac{7}{4}$, find the least common denominator (LCD) of 10 and 4, which is 20. 4. Convert each fraction to an equivalent fraction with denominator 20: $$\frac{23}{10} = \frac{23 \times 2}{10 \times 2} = \frac{46}{20}$$ $$\frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20}$$ 5. Now subtract the numerators: $$\frac{46}{20} - \frac{35}{20} = \frac{46 - 35}{20} = \frac{11}{20}$$ 6. The result is $\frac{11}{20}$, which is already in simplest form. Final answer: $\frac{11}{20}$